U.S. patent number 8,139,681 [Application Number 11/662,574] was granted by the patent office on 2012-03-20 for frequency error correction by using remodulation.
This patent grant is currently assigned to MStar France SAS, MStar Semiconductor, Inc., MStar Semiconductor, Inc., MStar Software R&D, Ltd.. Invention is credited to James Chapman, Navid Fatemi-Ghomi, Simon Richardson, Cyril Valadon.
United States Patent |
8,139,681 |
Chapman , et al. |
March 20, 2012 |
Frequency error correction by using remodulation
Abstract
A communications signal is received through a propagation
channel, down-converted in frequency and then converted into a
digital signal. The samples of the digital signal are processed to
estimate the information conveyed by the communications signal. The
estimated information is then used with knowledge about the
propagation channel to model the samples of the digital signal. The
modeled samples are compared with actual samples of the digital
signal to deduce phase errors in the digital signal. The phase
errors are then used to deduce a frequency error in the digital
signal that can be used to correct the samples of the digital
signal and to correct the down-conversion process.
Inventors: |
Chapman; James (Cambridge,
GB), Richardson; Simon (Egham, GB),
Valadon; Cyril (Letchworth, GB), Fatemi-Ghomi;
Navid (Frimley, GB) |
Assignee: |
MStar Semiconductor, Inc.
(KY)
MStar Software R&D, Ltd. (Shenzhen, CN)
MStar France SAS (Issy les Moulineaux, FR)
MStar Semiconductor, Inc. (TW)
|
Family
ID: |
33186854 |
Appl.
No.: |
11/662,574 |
Filed: |
September 9, 2005 |
PCT
Filed: |
September 09, 2005 |
PCT No.: |
PCT/GB2005/003486 |
371(c)(1),(2),(4) Date: |
September 06, 2007 |
PCT
Pub. No.: |
WO2006/027604 |
PCT
Pub. Date: |
March 16, 2006 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20080130729 A1 |
Jun 5, 2008 |
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Foreign Application Priority Data
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Sep 10, 2004 [GB] |
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0420186.9 |
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Current U.S.
Class: |
375/316;
455/150.1; 375/136; 375/347; 375/342; 370/208; 375/322; 370/206;
375/344; 370/210 |
Current CPC
Class: |
H04L
27/2277 (20130101); H04L 25/0224 (20130101); H04L
2027/0067 (20130101); H04L 2027/0095 (20130101); H04L
2027/0061 (20130101); H04L 2027/0055 (20130101); H04L
2027/0032 (20130101) |
Current International
Class: |
H03K
9/00 (20060101) |
Field of
Search: |
;375/242,245,250,259,295,306,316,327,350,371,375,135,137,146-150,260,267,296,322,342-346,353
;370/206,208,210,512 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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1392698 |
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Jan 2003 |
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CN |
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2262690 |
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Jun 1993 |
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GB |
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2394131 |
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Apr 2004 |
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GB |
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Other References
International Search Report dated Dec. 20, 2005. cited by other
.
Search Report under Section 17, dated Jan. 24, 2005. cited by
other.
|
Primary Examiner: Singh; Hirdepal
Attorney, Agent or Firm: Edell, Shapiro & Finnan,
LLC
Claims
The invention claimed is:
1. A system comprising: a receiver for acquiring a communications
signal, comprising a series of information symbols, through a
propagation channel; and an apparatus for deducing one or more
frequency error estimates from a digital signal produced by the
receiver to represent the communications signal, the apparatus
configured for analyzing the digital signal representing the
communications signal, comprising the series of information
symbols, that has been acquired by the receiver through the
propagation channel, the apparatus comprising: symbol estimation
means for processing samples of the digital signal to estimate
symbols of the communications signal; sample simulation means for
modeling at least one sample of the digital signal using the
estimated symbols and knowledge about the propagation channel;
phase error estimation means for comparing a modeled sample of the
digital signal with an actual sample of the digital signal to
estimate a phase error in the latter sample; frequency error
estimation means for estimating a frequency error from phase errors
produced by the phase error estimation means, wherein each phase
error produced by the phase error estimation means is made
available for correction of the digital signal sample, if any, that
follows the digital signal sample on which the phase error was
estimated, wherein the receiver comprises frequency conversion
means for down-converting the received communications signal in
frequency and frequency control means for controlling the frequency
conversion means on the basis of one or more frequency error
estimates.
2. The system according to claim 1, wherein the communications
signal contains a sequence of training symbols and the sample
simulation means only utilizes estimated symbols that lie close to
that training sequence.
3. The system according to claim 1, wherein the frequency error
estimation means uses a linear regression technique to calculate
the frequency error estimate.
4. The system according to claim 1, wherein the frequency error
estimation means discriminates noisy phase errors and excludes them
from the frequency error estimation.
5. The system according to claim 1, further comprising means for
correcting samples of the digital signal on a basis of one or more
frequency error estimates produced by the frequency error
estimation means.
6. A signal processing method comprising: receiving a
communications signal, comprising a series of information symbols,
through a propagation channel; and deducing one or more frequency
error estimates from a digital signal produced to represent the
communications signal by analyzing the digital signal representing
the communications signal, comprising the series of information
symbols, that has been acquired by a receiver through the
propagation channel, the method comprising: a symbol estimation
step comprising processing samples of the digital signal to
estimate symbols of the communications signal; a sample simulation
step comprising modeling at least one sample of the digital signal
using the estimated symbols and knowledge about the propagation
channel; a phase error estimation step comprising comparing a
modeled sample of the digital signal with an actual sample of the
digital signal to estimate a phase error in the latter sample; and
a frequency error estimation step comprising estimating a frequency
error from phase errors produced by the phase error estimation
step, wherein each phase error that is estimated is made available
for the correction of the digital signal sample, if any, that
follows the digital signal sample on which the phase error was
estimated, wherein the process of receiving the communications
signal comprises a frequency conversion step for down-converting
the received communication signal in frequency and the frequency
conversion process is controlled on the basis of one or more
frequency error estimates.
7. The signal processing method according to claim 6, wherein the
communications signal contains a sequence of training symbols and
the sample simulation step only utilizes estimated symbols that lie
close to that training sequence.
8. The signal processing method according to claim 6, wherein the
frequency error estimation step uses a linear regression technique
to calculate to the frequency error estimate.
9. The signal processing method according to claim 6, wherein the
frequency error estimation step discriminates noisy phase errors
and excludes them from the frequency error estimation.
10. The signal processing method according to claim 6, further
comprising a correcting step for correcting samples of the digital
signal on a basis of one or more frequency error estimates produced
by the frequency error estimation step.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a National Phase Application of
PCT/GB2005/003486, which claims priority to GB 0420186.9, which is
hereby incorporated by reference.
BACKGROUND OF THE INVENTION
For most types of mobile communication system to operate
satisfactorily, it is required that the receiver is locked in time
and frequency to the transmitter. Traditionally, the receiver
achieve-frequency synchronism with the transmitter by controlling
the frequency of a local oscillator used to down-convert the signal
from RF to base-band (or IF depending on the radio
architecture).
FIG. 1 depicts various processing stages that form part of such an
approach. Indeed, FIG. 1 can be taken to represent a view into the
signal processing chain of a mobile telephone or a cellular
communications network base station. It should be noted that the
blocks shown in FIG. 1 represent processing operations performed on
a received signal but do not necessarily correspond directly to
physical units that may appear within a practical implementation of
a receiver. The first stage 101 corresponds to the radio frequency
processing. During the radio frequency processing, the received
signal is down-converted to base-band using a mixer 103. The
reference frequency used to drive the mixer is generated by an
oscillator 104. Following this carrier down-conversion, the signal
is low-pass filtered 102 and then passed to the mixed-signal
processing stage 108. The mixed signal processing includes
Analogue-to-Digital Conversion (ADC) 105, sampling 106 and low pass
filtering 107. The resulting signal, which is now digital, is
supplied to the digital signal processing stage 109 where it is
buffered in preparation for processing. The demodulation stage 110
produces estimates of the transmitted information bits. As part of
the digital signal processing, estimates of the residual frequency
offset in the digital signal are produced. Those frequency error
estimates are filtered at 111 in order to improve their accuracy
and used to control the frequency reference produced by the
oscillator 104.
This frequency locking mechanism is typical of mobile communication
receivers and achieves synchronism through a feedback loop. Such an
approach is very effective in conditions where the frequency
reference of the transmitter is stable over time. However, such
stability cannot always be achieved. For example in cellular
communication systems, the hand-over of a user between different
base-stations will result in a short term offset in the frequency
of the received signal. This frequency offset will usually be
relatively low (0.1 parts per million is a typical value) but can
negatively impact on the performance of the demodulation of the
signal within the receiver, especially when a high order modulation
scheme is used. For example, the performance of the 8PSK modulation
used by the E-GPRS (Enhanced General Packet Radio Service) system
will be affected by such a small residual frequency offset. In
order to limit the performance degradation that such a residual
frequency offset causes to the information link, a correction of
the receiver frequency reference should be made as quickly as
possible. The mechanism described in FIG. 1 is therefore not
suitable since the feedback loop introduces a delay in the
correction made to the signal.
One possible mechanism to correct this residual frequency offset is
depicted in FIG. 2. It can be seen that this approach is similar to
the one presented in FIG. 1. However, an extra processing stage has
been introduced in the digital signal processing section 209. The
digital signal produced by the mixed-signal processing stage 208 is
buffered and first processed by the `estimate and correct frequency
error` unit 211. The resulting signal, from which the residual
frequency offset will have ideally been removed, is then
demodulated 210. The `estimate and correct frequency error` unit
uses the buffered received signal to first estimate the residual
frequency offset. Once this frequency offset has been estimated, a
phase correction to the received signal is performed in order to
remove it. The residual frequency offset in the received signal can
be estimated using frequency component analysis techniques.
However, because the residual frequency offset is low compared to
the sampling frequency, a large number of samples is usually
required in order to obtain an accurate estimate.
BRIEF SUMMARY OF THE INVENTION
According to one aspect, the invention provides apparatus for
analysing a digital signal representing a communications signal,
comprising a series of information symbols, that has been acquired
by a receiver through a propagation channel, the apparatus
comprising symbol estimation means for processing samples of the
digital signal to estimate symbols of the communications signal,
sample simulation means for modelling at least one sample of the
digital signal using estimated symbols and knowledge about the
propagation channel and phase error estimation means for comparing
a modelled sample of the digital signal with an actual sample of
the digital signal to estimate a phase error in the latter
sample.
The invention also relates to a method of analysing a digital
signal representing a communications signal, comprising a series of
information symbols, that has been acquired by a receiver through a
propagation channel, the method comprising a symbol estimation step
comprising processing samples of the digital signal to estimate
symbols of the communications signal, a sample simulation step
comprising modelling at least one sample of the digital signal
using estimated symbols and knowledge about the propagation
channel, and a phase error estimation step comprising comparing a
modelled sample of the digital signal with an actual sample of the
digital signal to estimate a phase error in the latter sample.
Thus, the invention provides a way of quantifying phase errors in a
communications signal acquired by a receiver. Such errors may be
attributable, at least in part, to imperfect frequency conversion
of the acquired communications signal within the receiver.
If desired, estimated phase errors can be used to correct the
digital signal representing the acquired communications signal. In
certain embodiments, a phase error that is estimated from an actual
sample of the digital signal and a modelled sample of the digital
signal is used to correct the sample of the digital signal that
follows the sample that was used to produce the phase error
estimate.
In certain embodiments, phase error estimates are used to produce
estimates of a frequency error in the digital signal representing
the acquired communications signal. A frequency error estimate so
produced may be used to correct phase errors in the digital signal
and/or correct a frequency conversion process involved in the
production of the digital signal.
As mentioned earlier, the invention involves the estimation of
symbols of the communications signal. These estimated symbols can,
for example, be in the form of modulated symbols having complex
values or demodulated symbols represented by groups of bits.
The invention can be implemented by hardware or by software running
on a processor or by a combination of both. The invention can be
employed in a participant of a mobile communications network, such
as a base station or a hand set. In particular, the invention is
suited to use in a EGPRS system.
BRIEF DESCRIPTION OF THE DRAWINGS
By way of example only, certain embodiments of the invention will
now be described with reference to the accompanying drawings, in
which:
FIG. 1 presents a general mechanism for achieving frequency
synchronism of a receiver with a transmitter;
FIG. 2 presents a mechanism for achieving frequency synchronism of
a receiver with a transmitter in the case where a large number of
received samples are available;
FIG. 3 presents a decision-directed approach for the phase
correction of a received signal; and
FIG. 4 describes various computations performed in the approach
shown in FIG. 3.
DETAILED DESCRIPTION OF THE INVENTION
FIG. 3 gives an overview of a digital signal processing unit 301
that can be used in place of unit 109 to implement an embodiment of
the invention. As in FIGS. 1 and 2, the signal generated by the
mixed-signal processing is buffered within the digital signal
processing unit 301 in preparation for processing. Each decision
produced by demodulation unit 306 (analogous to unit 110) is
compared with the corresponding received sample to produce an
estimate of the latter's phase error, and hence current frequency
offset, using unit 303. Because the demodulation unit 306 will
introduce a delay in the generated decisions, a delay unit 302 is
required for the received samples. Filtering, or averaging, of
those frequency estimates is then performed by unit 304 in order to
improve the accuracy of those estimates. This filtered frequency
offset estimate is then used by unit 305 to correct the phase of
the received samples. Each decision produced by the demodulation
unit 306 is used as soon as available rather than at the end of the
whole information block. Hence, the frequency correction can be
applied to the received signal as soon as decisions are made by the
demodulation unit 306. The accuracy of this frequency correction is
then improved as more samples from the received signal are
processed.
In order to describe the computations performed by digital signal
processing stage 301, it is first useful to present the model of
the transmission link.
A transmission block {d.sub.k}.sub.k.epsilon.(1, . . . , D) is made
of D information bits d.sub.k.epsilon.{0,1}. These information bits
are first grouped into C sets of M bits (it is assumed that
D=M.times.C): .DELTA..sub.k={d.sub.M.times.k, . . .
,d.sub.(M.times.k)+(M-1)}
Each set of M information bits .DELTA..sub.k is modulated onto the
complex plane using a modulation scheme M that maps sets of M bits
on to the complex plane. For example, in the case of an 8PSK
modulation, the modulation M can be expressed as:
.function..DELTA..function..times..times..times..function.
.times..times..times..times. ##EQU00001##
A slightly modified version of the 8PSK modulation described by the
above equation is used in the E-GPRS system.
The C modulated symbols c.sub.k=M (.DELTA..sub.k) are then
transmitted over the air and in the process are distorted by the
propagation channel. Assuming a general model with memory for the
propagation channel, the samples {s.sub.k}.sub.k.epsilon.(1, . . .
, C) at the input of the receiver can be expressed as:
.function..xi..xi..function..xi. ##EQU00002## .xi..sub.k represents
the state (memory) of the propagation channel when the k.sup.th
modulated symbol is transmitted. Note that any filtering performed
by either the transmitter and/or the receiver can be incorporated
in the propagation channel model. The mappings F and S used to
model the propagation channel can be time varying. However, to
simplify the notations, it is assumed in this document that those
mappings do not depend on time.
At the receiver, the signal will be corrupted by noise and by the
effect of the residual frequency offset between the transmitter and
the receiver. Taking into account these effects, the signal which
is input to the digital signal processing unit 301 can be expressed
as: r.sub.k=e.sup.j.times..theta..sup.k.times.s.sub.k+n.sub.k where
{n.sub.k}.sub.kc(1, . . . , C) denotes the sequence of additive
noise samples and the e.sup.j.times..theta..sup.k multiplicative
term models the effect of the residual frequency offset on the
received signal. The phase offset on the k.sup.th sample can be
expressed as: .theta..sub.k=(k.times.)+.theta..sub.0 where denotes
the residual angular frequency offset and is related to frequency
error through:
.THETA..times..pi. ##EQU00003## where f.sub.s is the sampling
frequency.
The operation of the digital signal processing stage 301 in
correcting the residual phase offset in a received data stream will
now be described with the aid of FIGS. 3 and 4, the latter Figure
showing in more detail the operations that occur within the digital
signal processing stage 301.
After the reception of the k.sup.th complex sample r.sub.k, the
demodulator 306/401 produces an estimate of the transmitted symbol
.DELTA..sub.k-.delta.. The delay .delta. in the symbol decisions
produced by the demodulator 306/401 can be explained by the fact
that the propagation channel between the transmitter and the
receiver has memory. Hence, the transmitted information is spread
over multiple received symbols and the demodulator 306/401 will
usually combine the information in those different symbols in order
to improve its performance. The symbol decision produced by the
demodulation unit 306/401 is denoted {circumflex over
(.DELTA.)}.sub.k-.delta..
Using knowledge of the modulation used by the transmitter, the
digital signal processing stage 301 can then generate an estimate
of the transmitted complex symbol c.sub.k-.delta.. This estimated
complex symbol is denoted c.sub.k-.delta.. It should be noted that
the digital signal processing stage 301 may not have prior
knowledge of the modulation scheme M being used by the transmitter
and hence may have to deduce the modulation scheme from the signal
stream arriving from the mixed signal unit 108. This is the case
in, for example, the EGPRS system where the transmitter can select
between the GMSK and 8PSK modulation schemes without explicitly
providing this format information to the receiver.
Assuming that the digital signal processing stage 301 has knowledge
of the propagation channel conditions, modelled by the mappings F
and S, it is possible for the digital signal processing stage to
generate an estimate of the complex symbol s.sub.k-.epsilon.. This
estimate is denoted s.sub.k-.delta..
It should be noted that the digital signal processing stage 301
will usually not have prior knowledge of the propagation channel
conditions. However, it may be possible for the digital signal
processing stage 301 to generate an estimate of the channel
mappings. In this case, the digital signal processing stage 301 can
generate the complex symbol s.sub.k-.delta. using those estimates
rather than the true mappings. For example, in the EGPRS system,
the sequence of transmitted symbols includes a pattern, referred to
as training sequence, which is known to the receiver. The receiver
can use this training sequence to generate an estimate of the
propagation channel conditions.
If one assumes that the channel estimation is perfect, then the
symbol s.sub.k-.delta. corresponds to the received symbol
r.sub.k-.delta. a without additive noise or residual frequency
offset. This means that, if the noise in the received sample
r.sub.k-.delta. is ignored, the phase difference between the two
samples is equal to .theta..sub.k-.delta.. This relation can be
used to estimate the residual frequency offset.
One possible way to produce an estimate {circumflex over
(.theta.)}.sub.k-.delta. of the phase difference is through the
complex multiplication of the received symbol r.sub.k-.delta. with
the complex conjugate of the re-modulated symbol s.sub.k-.delta..
This modulation produces the following complex symbol:
p.sub.k=r.sub.k-.delta..times.s.sub.k-.delta.=e.sup.j.times..theta..sup.k-
-.delta..times.(s.sub.k-.delta..times.s.sub.k-.delta.)+(n.sub.k-.delta..ti-
mes.s.sub.k-.delta.)
If one ignores the noise term and assumes that the symbol
s.sub.k-.delta. was generated perfectly, the symbol p.sub.k can be
expressed as:
p.sub.k=e.sup.j.times..theta..sup.k-.delta..parallel.s.sub.k-.delta..para-
llel..sup.2
Hence, the estimate {circumflex over (.theta.)}.sub.k-.delta. can
be generated by computing the phase of the complex sample
p.sub.k.
It should be noted that a different set of computations could be
performed to estimate the phase difference {circumflex over
(.theta.)}.sub.k-.delta. from the received symbol r.sub.k-.delta.
and the re-modulated symbol s.sub.k-.delta..
One such alternative method will now be described in detail. In
this method, it is assumed that the phase error is small such that
the sine of the phase error can taken to be an approximation of the
phase error. Thus:
.theta..delta..apprxeq..function..function..function. ##EQU00004##
where Re(p.sub.k) and Im(p.sub.k) are the real and imaginary part
of p.sub.k. Within the digital signal processing stage 301, the
preceding equation can be implemented as a form of Taylor series
expansion as follows: {circumflex over
(.theta.)}.sub.k-.delta..apprxeq.Im(p.sub.k)(1+0.25.times.Z+0.09375.times-
.Z.sup.2+0.0390625.times.Z.sup.3+0.017089844.times.Z.sup.4+0.00769043.time-
s.Z.sup.5+0.00352478.times.Z.sup.6+0.001636505.times.Z.sup.7+0.000767112.t-
imes.Z.sup.8) where Z is defined as:
Z=2.times.(1-(Re(p.sub.k).sup.2+Im(p.sub.k).sup.2))
An estimate of the residual frequency offset can then be generated
from the phase difference estimates for a series of demodulated
symbols c.sub.k-.delta.. This estimate is denoted as {circumflex
over (.THETA.)}.sub.k. The estimated residual frequency offset and
the estimated phase difference are linked through the following
equation: {circumflex over
(.theta.)}.sub.k-.delta.=((k-.delta.).times.)+{circumflex over
(.theta.)}.sub.0
Hence the residual frequency offset can be estimated by performing
a linear regression on the phase difference estimates {circumflex
over (.theta.)}.sub.k-.delta.. If, for example, the linear
regression minimises the mean square error, the residual frequency
offset can be computed using the following equation
.THETA..times..delta..times..theta..times..delta..times..delta..times..th-
eta..delta..delta. ##EQU00005## where i=0 to k-.delta. and denotes
all of phase difference estimates calculated so far for the current
burst.
The initial phase {circumflex over (.theta.)}.sub.0 can be
estimated using the following equation:
.theta..times..delta..times..delta..times..delta..times..theta..times..de-
lta..times..delta..times..theta..delta..delta. ##EQU00006##
It is to be noted that this initial phase is re-estimated for each
new sample {circumflex over (.theta.)}.sub.i produced by the
demodulation unit 306/401.
The estimates of the residual frequency offset and the initial
phase {circumflex over (.theta.)}.sub.0 are then used to correct
the phase of the next received symbol to be processed by the
demodulation unit 306/401. This is achieved by arranging that the
next received symbol r.sub.k+1 to be processed by the demodulation
unit 306/401 is multiplied by the complex phasor:
e.sup.-j.times.(((k+1).times..sup.)+{circumflex over
(.theta.)}.sup.0.sup.)
At that point, assuming that the linear regression estimated
perfectly the residual frequency offset and the initial phase
{circumflex over (.theta.)}.sub.0, the modified symbol to be
processed by the demodulation unit does not have any phase
error.
For communication systems where the channel conditions are
estimated using a sequence of known transmitted symbols, it is
possible to improve the accuracy of the estimates of the residual
frequency offset and the initial phase {circumflex over
(.theta.)}.sub.0 by performing the linear regression using symbols
close to this training sequence first. In this case, the initial
phase {circumflex over (.theta.)}.sub.0 will be incorporated in the
model of the propagation channel. Moreover, because the initial
phase {circumflex over (.theta.)}.sub.0 does not need to be
estimated, the computational complexity is also reduced.
For example, in the EGPRS system, a sequence of 26 known symbols is
inserted in the middle of a burst of information. When symbols
close to the training sequence are used, the residual frequency
error can be estimated using the following equation:
.THETA..times..delta..times..theta..times..delta..times..delta..delta.
##EQU00007##
The phasor used to correct the phase of the next symbol to be
processed by the demodulation unit is then equal to:
e.sup.-j.times.(((k+1).times..sup.))
It should be noted that the quality of the samples {circumflex over
(.theta.)}.sub.i which are processed by the linear regression is
degraded by the noise that is present in the received signal data
stream. It is therefore possible to improve the accuracy of the
estimate by ignoring samples {circumflex over (.theta.)}.sub.i that
are deemed too noisy. For example, can be calculated using the
following equation:
.THETA..delta..times..lamda..theta..delta..times..lamda.
##EQU00008## where .lamda..sub.i{0,1} is a weight indicating
whether the phase sample {circumflex over (.theta.)}.sub.i is
excised or not. The preceding equation is based on the a priori
assumption that {circumflex over (.theta.)}.sub.0 is zero.
Different approaches can be taken to decide whether a phase sample
should be excised. For example, a sample {circumflex over
(.theta.)}.sub.i could be discarded (i.e., .lamda..sub.i set to 0)
if it is more than a given distance away from the line fitted to
the {circumflex over (.theta.)}.sub.i data by the linear
interpolation. Another option is to use any prior knowledge that
the receiver may have about the maximum that is possible for the
residual frequency error. For example, if the receiver knows that
.ltoreq. then it is possible to check that the current phase sample
{circumflex over (.theta.)}.sub.i lies within the region defined by
. Given a priori limits .ltoreq. it is possible to calculate the
line (of phase error versus received sample index) with the highest
allowable gradient (since the phase error for a given sample is
proportional to the sample index and the frequency offset--hence
the use of the linear regression to estimate the frequency error).
If the phase were estimated perfectly, the phase for the k.sup.th
sample would never be larger than (k.times.)+.theta..sub.0. Hence,
samples for which the phase estimate is larger than that can be
excised. It should be noted, however, that since in practice the
phase estimates will be noisy, only the samples which are larger
than the ideal maximum value plus a statistical margin should be
removed. It will also be understood that, since the frequency error
can be positive or negative, the region corresponding to valid
phase estimates needs to contain both positive and negative phase
estimates. Finally, the check on the phase error being lower than
the expected (k.times.)+.theta..sub.0 requires the knowledge of
.theta..sub.0. One solution is to use an up to date estimate of
.theta..sub.0 from the linear regression. Another solution is to
use a fixed, pre-defined, value.
FIG. 4 describes how the various computations described above are
put together in order to correct the residual frequency offset in
the received signal. The demodulation unit 401 provides estimates
of the transmitted information symbols {circumflex over
(.DELTA.)}.sub.k-.delta.. Those information symbols are then
modulated through unit 402. The channel mapping performed by unit
403 is then applied to those modulated symbols. This produces
estimates of the received symbols s.sub.k-.delta.. Those symbols
are combined with the received symbols s.sub.k-.delta.. The time
synchronism of those two data streams is achieved by the delay unit
404. The phase difference samples {circumflex over
(.theta.)}.sub.k-.delta. are computed by unit 405 and are then
processed by unit 406. Unit 406 performs the linear regression on
the phase difference samples (including, if desired, sample
excision) and produces an estimate of the residual frequency error
and, depending on the variant, the initial phase {circumflex over
(.theta.)}.sub.0. This information is then used by the phase
correction unit 408 to de-rotate the received symbol stream.
It should be noted that, in some cases, the modulation unit 402 and
the channel mapping unit 403 may not be required. This is the case
when the demodulation unit 401 outputs not only estimates of the
transmitted information symbols {circumflex over
(.DELTA.)}.sub.k-.delta. but also estimates of the modulated
symbols s.sub.k-.delta.. For example, if the demodulation technique
used within unit 401 is based on the Viterbi algorithm, the samples
s.sub.k-.delta. are usually required during the computations
performed to derive the information symbols {circumflex over
(.DELTA.)}.sub.k-.delta.. In such circumstances it is then not
necessary to replicate those computations in the modulation unit
402 and the channel mapping unit 403.
It should also be noted that the residual frequency offset estimate
used to perform the phase correction on the received symbols in
unit 408 can also be used to drive the feedback loop controlling
the local oscillator (unit 111 in FIG. 1).
* * * * *